Imaging device in a projection exposure facility

ABSTRACT

An imaging device in a projection exposure machine for microlithography has at least one optical element and at least one manipulator, having a linear drive, for manipulating the position of the optical element. The linear drive has a driven subregion and a nondriven subregion, which are movable relative to one another in the direction of a movement axis. The subregions are interconnected at least temporarily via functional elements with an active axis and via functional elements with an active direction at least approximately parallel to the movement axis.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/247,597, filed Oct. 8, 2008, which is a continuation of U.S. patentapplication Ser. No. 11/936,768, filed Nov. 7, 2007, which is acontinuation of U.S. patent application Ser. No. 10/250,495, filed onAug. 20, 2004, now U.S. Pat. No. 7,304,717, which is a National StageEntry of PCT/EP02/14380, filed on Dec. 17, 2002, which claims benefit ofDE 102 25 266.1, filed on Jun. 7, 2002, and of DE 101 62 289.9, filed onDec. 19, 2001.

BACKGROUND

1. Field of the Invention

The invention relates to an imaging device in a projection exposuremachine for microlithography, having at least one optical element and atleast one manipulator, having a linear drive, for manipulating theposition of the optical element.

2. Description of the Related Art

In the case of such imaging devices for projection exposure machines inlithography, also denoted lithographic optics for short, it is oftenadvantageous if individual optical elements can be positioned activelyduring adjustment and/or during operation, in order to set specificimaging properties and aberrations precisely. Thus, for example, inrotationally symmetrical imaging systems, adjusting optical elementswhile maintaining the rotational symmetry, for example in the case ofrotationally symmetrical refractive objectives, permits the displacementof lenses in the light direction (defined in the direction of thez-axis), the influencing of the focus, of the reduction ratio, of the3rd order distortion, of the field curvature, of linear coma and of theconstant spherical aberration. Moreover, environmental influences of arotationally symmetrical nature, for example a change in the atmosphericambient pressure, in the internal pressure, in the atmospheric humidityand in the temperature including longitudinal temperature gradients aswell as rotationally symmetrical components of the lens heating can becorrected, as is known from U.S. Pat. No. 4,961,001 and DE 37 33 823.

In the case of rotationally symmetrical imaging systems, adjustingoptical elements in conjunction with cancellation of the rotationalsymmetry and production of monochromatic symmetry for example in thecase of rotationally symmetrical refractive objectives, permits lensesto be displaced perpendicular to the z-axis, specifically in the x-yplane, also termed lens decentering, or the tilting of lenses about axesperpendicular to the light direction, and the exertion of influence oncentering errors that are expressed in nonrotationally symmetricalaberration profiles of monochromatic overall symmetry with reference topupil and field. Included therein are, for example, image offset,sagittal and tangential 2nd order distortion, linear image surface tiltand the constant coma. Furthermore, environmental influences ofmonochromatic symmetry, for example gradients of ambient pressure,internal pressure, air humidity and temperature perpendicular to thelight direction, can be corrected.

Moreover, it is very advantageous in catadioptric lithographic opticswith plane deflecting mirrors or beam splitter cubes to be able tomanipulate the position and tilting angles of the deflecting mirror orbeam splitter surfaces. For concave and convex reflecting surfaces incatadioptric or catoptric lithographic optics, it is also suitable tomanipulate the degrees of freedom in translation and tilting, in orderto be able to set rotationally symmetrical aberrations and centeringerrors precisely.

Such imaging devices with manipulators are known in this case from theprior art.

For example, details may be given here of such a manipulator with theaid of the design described in U.S. Pat. No. 5,822,133. The manipulatorthere is designed as a pure z-manipulator in the cases of applicationdescribed. This means that the manipulation is performed in thedirection of the optical axis normally denoted by “z”. The designcomprises two annular elements which are arranged one in another and canbe moved relative to one another by actuators over a range ofembodiments. Provided for guiding the parts relative to one another areleaf springs or, in accordance with a further refinement, diaphragmsthat are intended to ensure parallel movement of the two parts relativeto one another.

However, such a design has decisive disadvantages, depending onembodiment, in particular on the embodiment of the various actuatorsdescribed. Thus, for example, when pneumatic actuators are used it ispossible to achieve only a relatively low rigidity in design. Whenvibrations are correspondingly introduced, and when use is made of veryheavy optical elements, for example the very heavy lenses that are usedin microlithography or in astronomical applications, this low rigidityof the manipulator leads to severe disadvantages that have very negativeeffects on the imaging quality to be attained.

The use of hydraulic actuators is proposed in a further refinement. Itis certainly possible to attain a far higher rigidity with suchactuators than with the pneumatic actuators previously described.However, the hydraulic actuators harbor the risk of the components to bemanipulated being contaminated by the hydraulic fluid, in general anoil, should there be a leak. Such a contamination with hydraulic fluidis to be regarded as a severe disadvantage particularly in the case ofhigh-performance objectives such as are used, for example, inmicrolithography. Such objectives are usually filled with a defined gasmixture or else are evacuated, if appropriate. Should hydraulic fluid,in particular oil, pass into this ultraclean interior, this can pass asliquid or vapor into the region of the optical elements and be depositedon their surface. The imaging quality would then be severely degraded.The outlay on any possible cleaning would be extremely high.

Furthermore, appropriate actuators made from piezoelectric elements andlever gears are described in an alternative embodiment of theabove-named document. In this case, the levers of the gears can beinterconnected particularly via solid joints. This type of actuators canavoid the two above-named disadvantages. In this case, very goodresolutions can be achieved with these actuators. However, theseactuators have the severe disadvantage that they permit only a verysmall travel. Depending on application, in particular in the use,already mentioned repeatedly, in an imaging device for microlithography,the requirement for very good resolution is, however, mostlyadditionally accompanied by the requirement for a very large travel inrelation to the possible resolution. These requirements, which oftencannot be avoided for the purpose of attaining a very good imagingquality, cannot be attained by the design described in the above-namedUS document, and so said design disadvantageously fails to permit thedesired imaging quality.

Further manipulators, which have, however, the same or very similardisadvantages, are described, for example, by DE 199 10 947 A1. Thisdocument exhibits a design in which movement of the optical elementalong the optical axis is achieved via actuators, for examplepiezoelectric elements, and a corresponding gear made from leversconnected via solid joints.

A device for manipulating an optical element in a plane perpendicular tothe optical axis is specified, for example, by DE 199 10 295 A1. Thereis a need in this case for at least two actuators that, because of themovement accuracies to be attained with these actuators, act viaexpensive and complex lever devices on an inner ring of the mount thatcarries the optical element. In order to ensure a uniform and adequaterigidity of the lever devices, and thus of the joining of the two partsof the mount to one another, as well to ensure an adequate resolution ofthe movement, there is a substantial outlay with respect to production,in particular with respect to the observance of very narrowmanufacturing tolerances.

Furthermore, JP 3064372 discloses a device for manipulating opticalelements in the case of which a first group of optical elements and asecond group of optical elements are arranged such that they can bedisplaced along an optical axis by a manipulator. These two opticalgroups can also execute a tilting movement relative to the optical axiswith the aid of the manipulator device. Electrostrictive ormagnetostrictive elements can be used for the drives. The design of therotary actuators is not disclosed directly in an unambiguous fashion inthis document.

Reference may also be made regarding the further prior art to U.S. Pat.No. 6,150,750, which exhibits a linear drive for the field of electricalengineering, telecommunication engineering and automation. The lineardrive has a driven subregion and a nondriven subregion that can be movedrelative to one another in the direction of a movement axis, thesubregions being interconnected at least temporarily via piezoelectricelements that are designed in part as lifting piezoelectric elements andin part as shearing piezoelectric elements. The individual piezoelectricelement stacks, which comprise lifting and shearing piezoelectricelements in each case, can be brought by means of the liftingpiezoelectric elements into frictional grip relative to the drivensubregion, or can be raised thereby. The actual movement can then berealized via the shearing piezoelectric elements of those stacks thatare in frictional engagement. It is possible thereafter to conceive ofmoving on to other stacks, and so very large movement ranges can berealized.

This design of the linear drives results in practice in an actuator thatis capable, via its piezoelectric elements, of exerting holding forcesand forces in the direction of the movement axis on the two parts of thelinear drive. It is thereby possible to implement a linear stepper that,depending on the selection of the piezoelectric elements, has a verygood resolution and, on the basis of the possibility of moving on, alsohas a very large allowance for movement.

SUMMARY

It is the object of the invention to create an imaging device for aprojection exposure machine in microlithography comprising a manipulatorthat permits a very rigid configuration and a very good ratio ofresolution to lift for movements that are to be executed by themanipulator.

According to the invention, this object is achieved by virtue of thefact that for the manipulator use is made in the imaging device in theprojection exposure machine for microlithography of a linear drive thathas a driven subregion and a nondriven subregion, which are movablerelative to one another in the direction of a movement axis, thesubregions being interconnected at least temporarily via functionalelements with an active direction at least approximately perpendicularto the movement axis and via functional elements with an activedirection at least approximately parallel to the movement axis.

The design of the manipulator with the linear drive described aboveresults in an ideal manipulator for microlithography. In this case, thedirection in which the manipulation is to be performed and the number ofthe linear drives used in the manipulator are unimportant. Theadvantageous properties follow from the type of the linear drives perse.

Thus, depending on the functional elements used it is possible with theaid of the design to conceive, for example, of very high resolutions ofdown to a few fractions of nanometers, it also being possible to realizea very large extent of movement (range) through the possibility ofmoving on during the movement of the linear drive. Ratios of resolutionto range of the order of magnitude of 1:75 000 or better are conceivablein this case.

These ideal properties are associated with a very high adjusting speedof more than 5 μm/s in conjunction with a very high possible adjustingforce of more than 100 N.

The design of the linear drives themselves already allows a very highrigidity. The rigidity can often be raised further because of the factthat it is frequently possible to dispense with a gear.

Functioning as a whole takes place in this case virtually without thedevelopment of heat by the linear drive (Q<10 mW). This constitutes aparticular advantage in the case of use in the field of imaging devicesfor microlithography, since the development of heat and the thermalexpansion associated therewith can give rise to great problems withregard to dimensional accuracy and the accuracy to be attained.

Furthermore, the linear drives have a very long service life and a verysmall construction space given the known boundary conditions.

In accordance with a particularly advantageous development of theinvention, the functional elements are designed as piezoelectricelements.

Such a piezoelectric linear drive can in this case ideally fulfill thevery high and complex requirements that are set by the lithographicaloptics mentioned at the beginning.

The design of the functional elements now as shearing piezoelectricelements and now as lifting piezoelectric elements permits a veryaccurate infeed in the case of holding lifting piezoelectric elementsvia the resolution of the shearing piezoelectric elements, which is highin principle. The typically required positioning accuracies in the rangeof a few hundredths of nanometers to a few nanometers can thereby beattained. The typical optical element travels of the order of magnitudeof a few 10 to 100 μm can also be achieved without a problem through thepossibility of operating the linear drive in step mode. The accuracy ofthe total path traveled is also of the above-named order of magnitudeowing to the composition of the total path traveled from individualparts with the accuracy specified above. The piezoelectric linear drivestherefore achieve the ratio, resulting from the range of the aberrationsto be set and the required setting accuracy, of the maximum travel tothe required mechanical positioning accuracy of the order of magnitudeof 10⁵ to 10⁷.

Required positioning forces of the order of magnitude of 10 to 100 N,and holding forces below shock loading, for example in the case oftransport, which can be up to an order of magnitude higher, result fromthe masses of the optical elements to be manipulated and their mounts.The piezoelectric linear drives can likewise yield these holding andpositioning forces, as also a very high rigidity in the adjustingdirection. This high rigidity which, depending on the purpose of use,ranges from a few N/μm to a few 100 N/μm, permits a mechanical naturalfrequencies of the optical elements of a few hundred Hertz to beattained in a particularly advantageous way.

Because of the very high ratio of maximum travel to the requiredmechanical positioning accuracy of the piezoelectric linear drives, itis possible in a particularly favorable way for the latter to be ofgearless design. A return game can thereby be avoided, or at leastminimized, and parasitic movements in the directions perpendicular tothe desired direction of movement can be suppressed.

In order to be able to realize this in an ideal way, the drive must bearranged as close as possible to the optical element, and this in turnsubstantially restricts the construction space available. Thus, forexample, in the case of refractive systems it is advantageous for thedrive to be fully integrated into the cylindrical outer contour of theobjective. Owing to the very small design, possible in principle, of thepiezoelectric linear drives, the dimensions of each individual drive ineach direction are only a few centimeters. The integration is thereforeeasily possible in particular favorable way.

Integrating the piezoelectric linear drive into the lens mount alsoresults in the requirement for a low development of heat, since thermalexpansions and stresses in the region of the optical elements must beavoided at all costs, in order to achieve the appropriately high imagingquality required in the field of microlithography. As piezoelectricelements are known to have a low development of heat, it is possible toimplement heat developments of less than 10 mW in each of thepiezoelectric linear drives. The integration of the piezoelectric lineardrive into the imaging device in the region of the optical elementstherefore also does not constitute a problem from this point of view.

Adjusting speeds of a few μm/s between individual exposures aretypically required in the field of lithographic optics. Since theshearing piezoelectric elements can react very quickly, it is possibleto meet these requirements, since the adjustments are normally performedwith such small adjustment paths that the analog mode of thepiezoelectric linear drives, that is to say the pure adjustment via theshearing piezoelectric elements or a raising or sinking of the liftingpiezoelectric elements, is sufficient for the purpose.

By contrast, the entire traveling range is required over the entireservice life of a system of more than 10 years. This can be achievedwith the aid of the piezoelectric linear drives, since these canadvantageously hold their position at one end of the traveling rangewithout having to be permanently under electric tension for the purpose.Again, the average electric voltage across the piezoelectric lineardrives that is present over the service life can be selected to be lowwithout greatly impairing their mode of operation. This also has a veryadvantageous effect on the service life and the long term reliability.

It is, moreover, advantageous for transport that the piezoelectriclinear drive can be of self-locking design and is also designed inaccordance with the examples of application still to follow later, thatis to say can keep its position without the presence of a voltage.

The properties of the piezoelectric linear drive that have been statedabove ideally fulfill the requirements that must be fulfilled for thetasks of manipulation in a projection exposure machine formicrolithography. Here, these requirements are basically always the sameirrespective of the actual task of manipulation and the direction oftravel associated therewith. The use according to the invention of thepiezoelectric linear drive therefore opens up advantages with regard toall the requirements specified above in virtually all tasks ofmanipulation that can occur in such an imaging device, in particularwith regard to the manipulation of optical elements in the threeorthogonal x-, y- and z-directions, as well as with regard to instancesof tilting and/or rotation about these directions.

In an aspect, the disclosure features a manipulator for an opticalelement that is fitted on a movable part, the movable part and a fixedpart being connected via at least three bar elements that are linked viajoints to the movable part and to the fixed part, and that are arrangedat least approximately in one plane, and via three linear drives whosemovement axes are at least approximately perpendicular to the plane andwhose points of intersection with the plane form a triangle.

The joints can be designed as solid joints. All the bar elements can bearranged at least approximately in precisely one plane. All the barelements can be arranged at least approximately radially to the opticalaxis of the optical element.

In another aspect, the disclosure features a manipulator for an opticalelement that is fitted to a movable part, the movable part and a fixedpart being connected via an annular disk that is linked viacircumferential solid joints to the movable part and to the fixed part,and via three linear drives whose movement axes are at leastapproximately perpendicular to the plane of the annular disk and whosepoints of intersection with the plane form a triangle.

The movement axes can run at least approximately in the direction of theoptical axis of the optical element. The linear drives can have at leastone drive element. The linear drives can have at least one gear element.

Each of the linear drives can have a driven subregion and a non-drivensubregion, which move relative to one another in the direction of themovement axis, the subregions being at least temporarily connected toone another via functional elements with an active direction at leastapproximately perpendicular to the movement axis, and via functionalelements with an active direction at least approximately parallel to themovement axis.

The functional elements with the active direction at least approximatelyperpendicular to the movement axis can be designed as clamping elementsvia which it is possible to achieve clamping of the two subregionsagainst one another, or via which clamping of the two subregions appliedby a prestressing force can be released, and in that the functionalelements with the active direction at least approximately parallel tothe movement axis are designed as feed elements for moving the twosubregions against one another.

Each of the linear drives can have a parallel guide that guides the twosubregions at least approximately parallel to one another. The parallelguide can have two bars that are respectively connected via solid jointsto the subregions, and that are arranged at least approximately parallelto one another. The functional elements can be designed as piezoelectricelements. The functional elements with the active direction at leastapproximately perpendicular to the movement axis can be designed aslifting piezoelectric elements, and the functional elements with theactive direction at least approximately parallel to the movement axisare designed as shearing piezoelectric elements, the functional elementsbeing combined to form a number of piezoelectric stacks thatrespectively have lifting and shearing piezoelectric elements.

The connection of the movable part and of the fixed part via the lineardrives can be designed in such a way that one of the subregions ispermanently connected to the fixed part, and in that the other subregionis connected to the movable part in such a way that the connection isdecoupled with reference to movements perpendicular to the movementaxis.

The position of the movable part relative to the fixed part can bedetected via at least three sensors. The sensors can be designed atleast partially as absolutely measuring sensors. The sensors can bedesigned as optical position transducers. The optical positiontransducers can have a phase grating scale. The distances by which eachof the linear drives can be moved can be controlled or regulated as afunction of the position, detected by the sensors, of the movable partrelative to the fixed part.

Advantageous developments and refinements of the invention follow fromthe remaining subclaims and from the exemplary embodiments describedbelow in principle with the aid of the drawing, in which:

DESCRIPTION OF DRAWINGS

FIG. 1 shows a sketch of the principle of a projection exposure machinefor microlithography, which can be used to expose structures onto waferscoated with photosensitive materials;

FIG. 2 shows an illustration of the principle of the linear drive;

FIGS. 3 a to 3 f show an illustration of the functional principle of thelinear drive in accordance with FIG. 3;

FIG. 4 shows an illustration of the principle of a manipulator formanipulating an optical element in the direction of its optical axis;

FIG. 5 shows a plan view of the manipulator in accordance with FIG. 4;

FIG. 6 shows an illustration of the principle of a manipulator formanipulating an optical element in a plane perpendicular to its opticalaxis;

FIG. 7 shows an illustration of the principle of a possible apparatusfor manipulating a mirror about two axes, in a plan view; and

FIG. 8 shows a sectional illustration of the principle in accordancewith the line VIII-VIII in FIG. 7.

FIG. 9 a shows an illustration of an optical system with two lenses inthe case of uncorrected coma;

FIG. 9 b shows an enlarged section of the caustic of the comaillustrated in FIG. 9 a;

FIG. 10 a shows an illustration of the optical system known from FIG. 9a, in the case of approximately corrected coma;

FIG. 10 b shows an enlarged section of the caustic of the approximatelycorrected coma illustrated in FIG. 10 a;

FIG. 11 shows a plan view of an embodiment of a manipulator; and

FIG. 12 shows an enlargement of the detail in FIG. 4.

DETAILED DESCRIPTION

A projection exposure machine 1 for microlithography is illustrated inFIG. 1. Said machine serves for exposing structures on a substratecoated with photosensitive materials, which consists in generalpredominantly of silicon and is denoted as a wafer 2, for producingsemiconductor components such as, for example, computer chips.

The projection exposure machine 1 essentially comprises in this case anillumination system 3, a device 4 for holding and exactly positioning amask provided with a grating-type structure, a so-called reticle 5, bymeans of which the later structures on the wafer 2 are determined, adevice 6 for holding, moving on and exactly positioning this very wafer2, and an imaging device 7.

The basic functional principle provides in this case that the structuresintroduced into the reticle 5 are exposed onto the wafer 2, inparticular with a reduction in the structures to a third or less of theoriginal size. The requirements that are to be placed on the projectionexposure machine 1, in particular on the imaging device 7, with regardto the resolutions are in the sub-μm range in this case.

After exposure has been performed, the wafer 2 is moved on such thatthere are exposed on the same wafer 2 a multiplicity of individualfields, each having a structure prescribed by the reticle 5. Once theentire surface of the wafer 2 has been exposed, the latter is removedfrom the projection exposure machine 1 and subjected to a plurality ofchemical treatment steps, generally the removal of material by etching.If appropriate, a plurality of these exposure and treatment steps aretraversed one after another until a multiplicity of computer chips havebeen produced on the wafer 2. Because of the stepwise feed movement ofthe wafer 2 in the projection exposure machine 1, the latter isfrequently also denoted a stepper. By contrast, in the case of waferscanners the reticle 5 must be traveled over relative to the wafer 2 inorder thus to be able to image the reticle structure as a whole.

The illumination system 3 provides projection radiation required forimaging the reticle 5 on the wafer 2, only one projection beam 8 beingillustrated here for the principle, for example light or a similarelectromagnetic radiation. A laser or the like can be used as source forthis radiation. The radiation is shaped in the illumination system 3 viaoptical elements such that, upon impinging on the reticle 5, theprojection radiation has the desired properties with regard totelecentrism, uniform polarization, homogeneous transmission withreference to field and angle, the lowest possible coherence of the beamsrelative to one another, and the like.

An image of the reticle 5 is generated via the projection beam 8, and istransmitted, appropriately reduced, by the imaging device 7 onto thewafer 2, as has already been explained above. The imaging device 7,which can also be denoted objective, in this case comprises amultiplicity of individual reflective, refractive and/or diffractiveoptical elements such as, for example, lenses, mirrors, prisms, planeplates and the like.

Also part of the imaging device 7 is at least one manipulator 9, whichis indicated here only schematically. The manipulator serves tomanipulate the position of an optical element 10, to which it isconnected, in order to improve the achievable imaging quality. Themanipulator 9 in this case comprises a linear drive 11 with the aid ofwhich a part 12 of the manipulator 9 that is permanently connected tothe optical element and is movable relative to the imaging device 7 canbe moved relative to a part 13 permanently connected to the imagingdevice 7.

The linear drive 11, which is illustrated in principle in FIG. 2,comprises a driven subregion 14 and a nondriven subregion 15. Thenondriven subregion 15 is permanently connected to the fixed part 13, asis indicated here in principle. The driven subregion 14 is connected tothe movable part 12. The connection of the movable part 12 and thedriven part 14 is realized in this case via a pin 16, located in a bore,in such a way that the connection is decoupled with reference tomovements perpendicular to the movement axis 17 of the linear drive 11.

The connection of the driven subregion 14 and the nondriven subregion 15is performed in the case of the linear drive 11 in the embodimentillustrated here via eight different functional elements, of which atleast four temporarily interconnect the two subregions 14, 15 byfrictional grip. In each case four of the functional elements aredesigned such that they have an active direction perpendicular to themovement axis 17. These functional elements are marked in FIGS. 3 a-3 fby the reference numeral 18. Further functional elements, whose activedirection runs in the direction of the movement axis 17, are locatedbetween these functional elements 18 and the driven subregion 14 as wellas the nondriven subregion 15. These further functional elements aremarked by the reference numeral 19.

In accordance with a particularly favorable embodiment, the functionalelements 18, 19 can be designed as piezoelectric elements. Thefunctional elements denoted by the reference numeral 18 could then bedesigned as lifting piezoelectric elements 18, while the functionalelements denoted by the reference numeral 19 are implemented as shearingpiezoelectric elements 19. This results in the possibility of a movementcycle such as will be explained further later in the context of FIG. 3 ato FIG. 3 f.

As is indicated in the exemplary embodiment illustrated here, it ispossible to avoid parallel guidance between the two subregions 14, 15 inorder to achieve a parallel movement in the direction of the movementaxis 17 of the driven subregion 14 relative to the nondriven subregion15. In accordance with the embodiment illustrated here, the parallelguidance comprises two bars 20 that are respectively connected viajoints, in particular via solid joints, to the driven subregion 14 andthe nondriven subregion 15. This ensures that the driven subregion 14 ismoved in a parallel fashion relative to the nondriven subregion 15, thatis to say executes a movement in the direction of the movement axis 17.

The movement cycle of the linear drive 11 is explained in more detailbelow with reference to the following FIGS. 3 a to 3 f.

FIG. 3 a shows the driven subregion 14 and the nondriven subregion 15,together with the functional elements 18, 19, in an illustration of theprinciple. The driven subregion 14 is clamped in relation to thenondriven subregion 15 via the four lifting piezoelectric elements 18.The following step in the movement cycle is illustrated in FIG. 3 b, inwhich two of the lifting piezoelectric elements 18 are opened, that isto say no longer in engagement, such that it is possible to move thedriven subregion 14 relative to the nondriven subregion 15 by means ofthe two shearing piezoelectric elements 19 arranged in the region of thestill clamping lifting piezoelectric elements 18. This movement isillustrated in principle in FIG. 3 c. FIG. 3 d shows the next step if avery large movement of the driven subregion 14 relative to the nondrivensubregion 15 is desired. The driven subregion 14 is securely clampedagain by a renewed actuation of the lifting piezoelectric elements 18.The clamping via the two other lifting piezoelectric elements 18 is nowreleased, as is to be gathered from FIG. 3 e. FIG. 3 f then illustratesthe next step, in which the driven subregion 14 is moved on in turn viathe actuation of the shearing piezoelectric elements 19.

This principle of the movement cycle can be repeated as desired andexecuted in any desired directions. In the clamped state, the lineardrive 11 in this case respectively has a very high accuracy of movement,which stems from the accuracy of the shearing piezoelectric elements 19.In addition to this very high accuracy, it is also possible to realize avery large movement range via the possibility of moving on by means ofthe lifting piezoelectric elements 18, such that it is possible here toimplement an ideal ratio of resolution to movement range.

It is fundamentally possible in this case to conceive of different typesof actuation of the linear drive 11 of the type described above. Ifself-locking of the linear drive 11 is desired, the latter can bedesigned such that the functional elements 18, 19 are prestressed viaspring means (not illustrated here) against the driven subregion 14.This ensures that the functional elements 18, 19 are always, that is tosay in the case of non-actuation, in frictional engagement, and thussecure the position of the driven subregion 14 relative to the nondrivensubregion 15 by clamping. By actuating the lifting piezoelectricelements 18, this clamping can then be cancelled in the region of theseactuated lifting piezoelectric elements 18 to such an extent that thereis no longer a frictional connection here between the driven subregion14 and the nondriven subregion 15. The further cycles could then berealized as already described above. This design is particularlyfavorable in addition, since the service life of the piezoelectricfunctional elements 18, 19 can be lengthened by the prestressing thatcan be applied to the piezoelectric elements. However, another designwould also be conceivable in principle, in which clamping between thedriven subregion 14 and the nondriven subregion 15 is implemented onlygiven active energization of the lifting piezoelectric elements 18.

Such linear drives 11 are now suitable for the high requirements,already mentioned in the context of the introduction to the description,that are placed on tasks of manipulation in the region of imagingdevices 7, irrespective of whether what is involved is a manipulationperpendicular to the optical axis, a tilting manipulation or amanipulation in the plane perpendicular to the optical axis. On thebasis of this very general applicability of the above-named lineardrives 11 with their appropriate action for virtually all the areas ofmicrolithography in which elements participating in thephotolithographic process are to be manipulated with regard to theirposition, the aim in the following figures is to examine the principleof three examples, without intending to restrict the application of thelinear drives 11 to these specific tasks of manipulation from the fieldof an imaging device 7 for microlithography.

Illustrated in FIG. 4 is a cross section through the manipulator 9,which can be used for manipulating the optical element 10, a lens 10 inthe exemplary embodiment selected here, along its optical axis 21.Tilting of the optical element 10 is also conceivable in addition to apure movement in the direction of the optical axis 21, which is denotedin general by “z”.

For the purpose of manipulation, the movable part 12, here a movableinner ring that carries the optical element 10, is moved closer to thefixed part 13, here a fixed outer ring 13, connected to the imagingdevice 7, for example, via three of the linear drives 11, of which twoare visible here in principle.

In order to guide the movable part 12 relative to the fixed part 13,there is provided in the exemplary embodiment illustrated here anannular disk 22 that is connected via circumferential solid joints 23both to the fixed part 13 and to the movable part 12. The movable part12 can be moved relative to the fixed part 13 by the linear drives 11,whose movement axes 17 run at least approximately parallel to theoptical axis 21, the annular disk 22 achieving a guidance of the movablepart 13 such that the latter experiences no deflection in the planeperpendicular to the movement axes 17.

The exact design of the guides plays only a subordinate role for theexplanations present here, and so it is to be mentioned here only thatthe annular disk 22 per se is designed with a relatively large wallthickness. Consequently, virtually no deformations of any sort occur inthe annular disk 22. All the deformations that occur in the region ofsuch a guide element will take place in the region of thecircumferential solid joints 23. Since these solid joints 23 arearranged at very precisely defined positions, the behavior of such aguide element can be determined in advance exactly and very easily fromthe annular disk 22. Moreover, it is possible to implement a very highrigidity of the design, and thus a very high natural frequency.

A plan view of a the manipulator 9 thus designed is to be seen in FIG.5. Visible once again is the fixed part 13 and the movable part 12 withthe optical element 10. The guidance of the movable part 12 and thefixed part 13 is performed via the annular disk 22. Located in theregion below the annular disk 22 are the three linear drives 11, whichare indicated here in the form of a triangle. Visible in addition tothis are three sensors 24, which are indicated here in principle bymeans of oval structures. The sensors 24 are respectively arranged at anangle of 120° to one another and at an angle of 60°, respectively,relative to the linear drives 11. The exact position of the movable part12 relative to the fixed part 13 can be detected via the sensors 24. Thesensors 24 can be designed, for example, as optical sensors 24 that candetect an alteration in the position via a glass measuring scale, eitherincrementally or in absolute terms. Such sensors 24 are commerciallyavailable components, and for this reason their mode of operation is notto be examined here in more detail.

In conjunction with a very rigid design of the manipulator 9, thecombination of the three sensors 24, the three linear drives 11 and theannular disk 22 as guide permits an exactly controllable positioning ofthe optical element 10 in the direction of the optical axis 21 and/or atilting relative to the optical axis 21. The position of the opticalelement 10 in the plane perpendicular to the optical axis 11 is ensuredin this case by the guidance, the result being a design that is veryrigid and not susceptible to vibrations and/or excitation in the regionof the natural frequency.

In certain embodiments, in order to guide the movable part 12 relativeto the fixed part 13, at least three bar elements 115 are provided thatare connected in each case via joints 23 both to the fixed part 13 andto the movable part 12. The movable part 12 can be moved relative to thefixed part 13 by the linear drives 14, whose movement axes 17 run atleast approximately parallel to the optical axis 11, the bar elements115 achieving a guidance of the movable part 13 such that the latterexperiences no deflection in the plane perpendicular to the movementaxes 17.

A plan view of a manipulator 9 of such design is to be seen in FIG. 11.Visible once again is the fixed part 13 and the movable part 12 with theoptical element 10. The guidance of the movable part 12 and the fixedpart 13 is performed via three bar elements 115 that are indicated hereonly in principle. Located in the region below the bar elements 115 isin each case one of the linear drives 14, which are indicated here inthe form of a triangle. Visible in addition to this are three sensors24, which are indicated here in principle by means of oval structures.The sensors 24 are respectively arranged at an angle of 120° to oneanother and at an angle of 60°, respectively, relative to the lineardrives 14. The exact position of the movable part 12 relative to thefixed part 13 can be detected via the sensors 24. The sensors 24 can bedesigned, for example, as optical sensors 24 that can detect analteration in the position via a glass measuring scale, eitherincrementally or in absolute terms. Suitable principles are known forthe sensors 24, and for this reason their mode of operation is not to beexamined here in more detail.

FIG. 12 shows a detailed section through one of the bar elements 115 orthrough the annular disk 22. Both elements 115, 22 are of at leastapproximately identical design in cross section, since in the case ofthe use of bar elements 22, as well, it is very favorable to use solidjoints as joints 23 because of the stiffness that is to be achieved.

Visible in the illustration in accordance with FIG. 12 are the fixedpart 13 and the movable part 12, which are connected to one another viathe bar element 115 and the annular disk 22. As guide element, such adesign composed of bar element 115 and annular disk 22 which are pivotedat the two parts 12, 13 to be guided via the joints and solid joints 23exhibits very favorable mechanical properties. The bar element 115 orthe annular disk 22 is designed per se with such a large wall thicknessthat virtually no deformations of any sort occur in practice in the barelement 115 or the annular disk 22. All the deformations that occur inthe region of such a guide element will take place in the region of thejoints 23. Since these joints 23, in particular when they are designedas solid joints, are located in a fashion arranged at very exactlydefined positions, the behavior of such a guide element can bedetermined in advance very exactly and very easily from a number of thebar elements 115 or from one annular disk 22. Moreover, it is possibleto implement a very high rigidity of the design, and thus a very highnatural frequency.

The manipulator 9, which is designed in the way just described, canfulfill the very high requirements that occur in the region of theprojection exposure machine 1 for microlithography, and here, inparticular, in the imaging device 7. The ideal supplement to such adesign is in this case the linear drives 11 which, on the one hand, havea very high accuracy and which, on the other hand, permit a very largerange, that is to say the possibility of a very large movement stroke.In the case of such a z- and/or tilting manipulator 9 for use inmicrolithography, the necessary requirements placed on the resolutionare around 0.3 to 0.8 nm for a travel of ±80 to 200 μm. The rigidity tobe attained should here in any case be greater than 12-18 N/μm. Therequired adjusting forces are above 100 N in this case, but this is nota problem for the linear drives 11. The design of the linear drives 11must permit self-locking for this case of use, which is possible withouta problem in the ideal case with an appropriate prestressing of thepiezoelectric elements 18, 19, as has already been described above. Theself-locking must also hold forces of the order of magnitude of 6 to 8times the adjusting forces, for example in the case of shock loading.

All these preconditions are achieved ideally by the combination inaccordance with the above-described design.

In addition to the lens described in the above exemplary embodiment asoptical element 10, a comparable design is, of course, also conceivablewith other optical elements 10, for example a mirror. In the case of asomewhat coarser resolution and a larger travel range, generallycomparable boundary conditions obtain for such a purpose of use.However, the required rigidity must be still higher here. However, inconjunction with the coarser resolution of approximately 8-12 nm, thiscan be attained by the appropriate design of the solid joints in theregion of the blanks 20.

FIG. 6 shows a plan view of a further embodiment of the manipulator 9,here for the purpose of manipulating the optical element 10 in a planeperpendicular to the optical axis 21. The optical element 10, here alens, for example, is supported via lugs in a way known per se in afashion decoupled from deformation in the inner ring, that is to say themovable part 12 of the manipulator 9. The fixed part 13, that is to saythe outer ring here, and the inner ring 12 are designed in one piece inthe example illustrated here, a flexible connection between the innerring 12 and the outer ring 13 being created via a system ofcircumferential slots 25 between the inner ring 12 and the outer ring 13with interposed connecting elements 26 in the shape of an L. Theconnecting elements 26 in the shape of an L are designed as solidjoints. In addition to a pivot joint 27 and two of the linear drives 11,which are indicated here in principle, they constitute the soleconnection between the inner ring 12 and the outer ring 13.

The circumferential slots 25, which are introduced into the single-piecebasic form by means of separating cuts, are interrupted at regularintervals by two separating cuts, arranged next to one another at aslight spacing, in the shape of an L, the result being to form theconnecting elements 26 as webs between the cuts in the shape of an L.Moreover, the pivot joint 27 is likewise formed by offsetting andoverlapping the circumferential slots 25, the pivot joint 27 having aweb between the circumferential slots 25, which overlap each other inthis region. Instead of the unipartite nature of inner ring 12 and outerring 13 illustrated here, it is also, however, possible for theconnection to be effected via joints in the form of components that arewelded in, bonded or soldered.

The circumferential slots 25 are interrupted at two opposite points withthe formation of a relatively large cutout (not to be seen here) betweenthe outer ring 13 and the inner ring 12. One of the linear drives 11 isarranged in each case in the two cutouts. Here, in each case the drivensubregion 14 is connected to the outer ring 13 and the nondrivensubregion 15 is connected to the inner ring 12. This design, which isnot to be seen in detail in the illustration of the principle inaccordance with FIG. 6, can also be designed in exactly the oppositeway, without altering the mode of operation of the manipulator 9. Themanipulator 9 is designed as a construction having optimized forceclosure and safety.

The following conditions and/or assignments are to be observed in orderto achieve a desired and predetermined displacement of the inner ring 12relative to the outer ring 13 in the x-/y-plane:

The pivot joint 27 is to be arranged between the two points of action ofthe linear drives 11 for displacing the inner ring 12 in such a way thatthe tangents T₁ and T₂ at the points of action of the movement axes 17of the linear drives 11 intersect the tangent T₃ applied at the pivotjoint 27. The two points of intersection in this case form, firstly, acenter of rotation 28 for one of the linear drives 11 for displacing theinner ring 12 in the x-direction and, secondly, a center of rotation 29for the displacement of the inner ring 12 in the y-direction by theother one of the linear drives 11. It is to be ensured at the same timethat the two radials 30 and 31 from the center of rotation 28 and,respectively, the center of rotation 29 to the mid-point or to theoptical axis 21 are at right angles to one another. At least in a smallregion 32 (see the dashed illustration in FIG. 6) around the opticalaxis 21, the two radials 30 and 31 therefore form the two adjustingaxes, the radial 31 defining the x-axis and the radial 30 the y-axis.

Given an actuation of the first linear drive 11, the inner ring 12therefore rotates about the center of rotation 28, while given anadjustment of the second linear drive 11, the inner ring 12 rotatesabout the center of rotation 29. This means that, strictly speaking, nolinear x-movement or y-movement would result, but since the radii of theradials 30 and 31 are substantially greater than the envisaged adjustingmovement, a quasi-linear movement in the x-y plane results in the region32 already mentioned above, which corresponds to a travel area of theinner ring 12. In order to reset adjusting movements and to increase therigidity for additional and special loads, it is possible, ifappropriate, for leaf springs (not illustrated) to act respectively onthe inner ring 12 which are supported with their other ends on the outerring 13.

The arrangement and configuration of the circumferential slots 25 andthe connecting elements 26 results in a high elasticity in the plane(x-y plane) perpendicular to the optical axis 21 (z-axis). Moreover, ahigh rigidity is provided in the z-direction. This is based, inter alia,on the L shape of the connecting elements 26, which can have anappropriate length in the z-direction and consequently ensure a highrigidity in the z-direction. Just like the connecting elements 26, thepivot joint 27 constitutes a solid joint in the exemplary embodiment. Ofcourse, however, yet other types of joint are also possible forimplementing the displacement of the inner ring 12 relative to the outerring 13. In particular, the use of a third linear drive 11 instead ofthe pivot joint would also be conceivable here. The angular position ofthe two axes x and y in the plane defined by them could thereby bevaried.

If there is no wish for the ability to travel at right angles, theabove-named assignments of the centers of rotation 28, 29 and the pivotjoint 27 as well as, if appropriate, of a third linear drive 11 can alsobe made otherwise.

The manipulator 9, which is designed in the way just described, canfulfill the very high requirements that occur in the region of theprojection exposure machine 1 for microlithography, and here, inparticular, in the imaging device 7. The ideal supplement to such adesign is in this case the linear drives 11 which, on the one hand, havea very high accuracy and which, on the other hand, permit a very largerange, that is to say the possibility of a very large movement stroke.In the case of such an x/y manipulator 9 for use in microlithography,the necessary requirements placed on the resolution are around 15 to 25nm for a travel of ±1 to 2 mm. The rigidity to be attained should herein any case be greater than 5 N/μm. The required adjusting forces areabove 30 N in this case, but this is not a problem for the linear drives11. The design of the linear drives 11 must permit self-locking for thiscase of use, which is possible without a problem in the ideal case withan appropriate prestressing of the piezoelectric elements 18, 19, as hasalready been described above. The self-locking must also hold forces ofthe order of magnitude of 6 to 8 times the adjusting forces, for examplein the case of shock loading.

All these preconditions are achieved ideally by the combination inaccordance with the above-described design.

There is now described in FIG. 7 a further manipulator 9 that serves formanipulating the optical element 10, a mirror in the present case. Thedesign of the manipulator 9 is simplified in this case very stronglydown to the basic principles and includes a cardanic suspension of theoptical element 10 in the exemplary embodiment illustrated here. Thecardanic suspension of the optical element 10 in the manipulator 9 isintended in this case only as example of the principle for all types ofmanipulators 9 in the case of which linear drives 11 move the opticalelement about a fixed bearing point—thus, in general, a tilting of theoptical element 10.

Moreover, in addition to the plane mirror illustrated here the opticalelement 10 can also be a concave mirror, a prism, a beam splitter cubeor the like, whose manipulation, in particular tilting manipulation, isdesired for optimizing the mode of operation of the imaging device 7 ofthe projection exposure machine 1.

The manipulator 9 in accordance with the exemplary embodimentillustrated in FIG. 7 and FIG. 8 is designed in this case such that theoptical element 10 is permanently connected to the movable part 12which, in turn, is connected to a movable intermediate frame 34 viabearing and pivot points 33. This intermediate frame 34 is connected tothe fixed part 13 of the manipulator 9 via two further bearing and pivotpoints 35. The perpendicular arrangement, visible in FIG. 7, of theconnecting lines of the respective bearing points 33, 35 relative to oneanother results in a cardanic suspension that is known per se andpermits a tilting of the optical element 10 with regard to the opticalaxis 21 to be seen in FIG. 8. In this case, the required linear drives11 are indicated in principle in FIG. 7 via the triangles in a similarway as has already been done for the preceding figures.

In the principle of the cross section in accordance with FIG. 8, thelinear drives 11 with their movement axes 17 are illustrated once morein greater detail. It may be seen that the movable intermediate frame 34can be manipulated about the axis of rotation formed by the bearingpoints 35 via one of the linear drives. In the exemplary embodimentillustrated here in principle, there is indicated a spring device 36that presses the intermediate frame 31 against the linear drive 11 andthus permits a continuous resetting and zero-backlash connection betweenthe linear drive 11 and the intermediate frame 34. The linear drive 11also to be seen between the intermediate frame 34 and the movable part12 functions in a similar way. Of course, it would also be conceivableto implement the restoring force with other means. For example, thegravitational force could be used for resetting in the case of aneccentric arrangement of the axis of rotation.

The design described by FIGS. 7 and 8 is intended in this case toindicate the possibilities of the use of the linear drive 11 only inprinciple; it is, of course, also possible to conceive of any otherdesigns in the case of which either one or more of the linear drives 11serve as bearing points, as has been described in the preceding figures,or in the case of which the linear drives 11 are used to manipulate theoptical element 10 about one or more fixed fulcrums or bearing points33, 35.

The following FIGS. 9 a to 10 b describe a further possibility ofachieving an even higher imaging quality in the area of the imagingdevice 7.

An analysis, carried out by the inventor, of the aberrations owing tolens heating revealed that in the case of an optical system with anoff-axis field it is not the dichromatic aberrations such as anamorphicdistortion that supply the largest fraction of the errors after therotationally symmetric errors such as, for example, field curvature orastigmatism with a square field profile, but the monochromaticaberrations, for example the sagittal and tangential distortion and theconstant coma. The following discussion relates to the coma.

FIG. 9 a shows an optical system that is formed from two lenses 10 and10′. The beam path through the lenses 10 and 10′ is illustrated startingfrom an object point O. A diaphragm 37 is provided to delimit the lightbundle. In this example, the lens 10′ is tilted by approximately 12°about an axis perpendicular to the optical axis 21. After the lightbeams have passed through the two lenses 10 and 10′, the beams shouldintersect again at an image point O′. In addition to other aberrations,the tilting of the lens 10′ induces coma for the axial point O′.

An enlarged illustration of the caustic about the image point O′ isillustrated in FIG. 9 b. It is now clearly to be seen here that theobject point O cannot be imaged in a punctiform fashion by the twolenses 10 and 10′ in conjunction with tilting of the lens 10′. A mainbeam 38 and edge beams 39 do not meet at the focal point or image pointO′. The result is an asymmetric and unsharp image of the object point O′that resembles a comet's tail and is also denoted coma.

In order to correct these aberrations as well as the transversedistortion, it is now possible to make use of the possibility of tiltingthe newly developed Z manipulator 9 in accordance with the invention.This is implemented in FIG. 10 a, in which the lens 10 is to be designedhere as a Z manipulator. An illustration of the Z manipulator 9 inconjunction with the lens 10 has been dispensed with in this exemplaryembodiment for the purpose of simplifying the illustration of the beampath. The lens 10 is now tilted by 0.75°. As is illustrated in FIG. 10b, this design of the optical system compensates to a large extent thecoma induced on the optical axis 21 by the tilting of the lens 10′. Theenlarged caustic in accordance with FIG. 10 b demonstrates a virtuallycorrected coma, since the main beam 38 and the edge beams 39 intersectat the image point O′. As is to be expected for this system, otheraberrations occur owing to the strong tilting of the two lenses 10 and10′. However, this can be avoided by means of simulation calculationsperformed in advance with the aid of optical computer programs.

Specifically, aberrations owing to asymmetric lens heating, such as theconstant coma or the transverse distortion, can now be corrected bydisplacing lenses 10 perpendicular to the optical axis 21 or by tiltinglenses 10.

Depending on the purpose of application, the lenses to be manipulatedare intended specifically for a particular design. In the case ofconduct of a sensitivity analysis, and with the aid of its results, itis possible to select lenses that are suitable both as Z manipulators 9and for correcting monochromatic errors (coma, distortion) by tilting.Their use leads to a substantially improved imaging quality.

The Z manipulator 9 according to the invention additionally permits thecorrection of errors that are introduced inadvertently into the systemby the imperfect operation of the conventional manipulators.

It is therefore likewise possible now to correct even monochromaticaberrations with the aid of this manipulator type 9. The manipulationsof the lenses 10 can be performed individually or in combination byz-displacement of the lenses 10 along the optical axis 21 or by tiltingthe lenses 10. It is therefore now also possible to correct asymmetricaberrations that are caused by lens heating.

1. A system, comprising: an optical element; and a manipulator coupledto the optical element, wherein: the manipulator is configured so thatduring operation the manipulator varies the optical element; themanipulator has a resolution and a range; a ratio of the resolution tothe range is 1:75,000 or more; and the system is a microlithographyprojection system.
 2. The system of claim 1, wherein the resolution isfrom 0.3 nm to 0.8 nm.
 3. The system of claim 2, wherein the range isfrom +80 microns to 200 microns.
 4. The system of claim 1, wherein therange is from +80 microns to 200 microns.
 5. The system of claim 1,wherein: the manipulator comprises a first portion and a second portion;the first portion is fixed with respect to a frame of the system; thesecond portion is attached to the optical element; and the secondportion is linearly moveable with respect to the first portion.
 6. Thesystem of claim 5, wherein the manipulator further comprises one or morepiezoelectric elements that couple the first portion to the secondportion.
 7. The system of claim 6, wherein the piezoelectric elementscomprise shearing piezoelectric elements.
 8. The system of claim 6,wherein: the piezoelectric elements comprise a first piezoelectricelement and a second piezoelectric element; the first piezoelectricelement is positioned on a first side of the second portion; the secondpiezoelectric element is positioned on a second side of the secondportion; the first side of the second portion is opposite the secondside of the second portion; and during operation, the first and secondpiezoelectric elements clamp the second portion to position the secondportion relative to the first portion.
 9. The system of claim 8, whereinthe manipulator is within a space between the first and second portions.10. The system of claim 8, wherein the manipulator is integrated into amounting apparatus which mounts the optical element to a frame of thesystem.
 11. The system of claim 1, wherein the manipulator is acomponent of a mounting apparatus which mounts the optical element to aframe of the system.
 12. A machine, comprising: an illumination system;and a system according to claim 1, wherein the machine is amicrolithography projection exposure machine.
 13. A system, comprising:an optical element; a frame; and a mounting apparatus which couples theoptical element to the frame, the mounting apparatus comprising: a firstportion fixedly attached to the frame; a second portion fixedly attachedto the optical element; and a manipulator which couples the first andsecond portions, wherein: the manipulator is configured so that duringoperation the manipulator varies the optical element; the manipulatorhas a resolution and a range; a ratio of the resolution to the range is1:75,000 or more; and the system is a microlithography projectionsystem.
 14. A system, comprising: an optical element; a frame; a sensor;and a mounting apparatus which couples the optical element to the frame,the mounting apparatus comprising: a first portion attached to theframe; a second portion attached to the optical element; and amanipulator configured so that during operation the manipulator variesthe optical element, wherein: the manipulator has a resolution and arange; a ratio of the resolution to the range is 1:75,000; the sensor isconfigured to monitor a position of the optical element relative to theframe; and the system is a microlithography projection system.
 15. Thesystem of claim 14, wherein the sensor is an optical sensor.
 16. Thesystem of claim 15, wherein the optical sensor comprises a glassmeasuring scale.
 17. The system of claim 14, wherein the systemcomprises a plurality of sensors configured to monitor the position ofthe optical element relative to the frame, and the plurality of sensorsare arranged symmetrically with respect to an optical axis of thesystem.
 18. The system of claim 14, wherein the system comprises threesensors and three manipulators, and the three sensors and the threemanipulators are arranged symmetrically with respect to an optical axisof the system.
 19. The system of claim 14, wherein the sensor isconfigured to monitor an absolute position of the optical elementrelative to the frame.
 20. The system of claim 14, wherein the sensor isconfigured to monitor an incremental position of the optical elementrelative to the frame.